Epidemiology plays a major role in the identification of carcinogenic agents and in the quantification of dose time response relationships upon which regulation and preventive strategies are based. epidemiology as a science depends critically upon statistics. The goal of this project is the development of more efficient statistical designs and methods of analysis for both analytic and descriptive studies. There are three areas of emphasis. First, many studies involve the estimation of a large number of related quantities: multiple relative risks in case-control studies involving multiple diseases and multiple risk groups; multiple cancer rates in small areas used for construction of maps; and multiple individual responses to intervention in longitudinal studies. A major goal is the development, evaluation and implementation of hierarchical statistical models that allow for the efficient estimation of such related quantities. Second, two-phase case-control studies and other complex stratified designs are of great value in limiting the collection of costly covariate data to those subjects who are most informative regarding disease/risk factor associations. An important example is the validation substudy conducted to alleviate the effects of measurement error. Optimal methods for design and analysis of data from such complex designs will be developed. Finally, epidemiologists have proposed new study designs that involve comparison of the exposures of diseased cases with those of internal or artificial controls. Examples are the haplotype relative risk method in genetic epidemiology, the case-specular design for study of electromagnetic fields of cancer, and the case-crossover and case-time-control designs for studies of the effects of intermittent exposures on event rates. Unfortunately, misleading inferences occur when these methods are used in situations that do not meet the underlying assumptions. A critical evaluation is planned of the logical foundations of such case "pseudo-control" designs, with a goal of maximizing the validity and efficiency of inferences based upon them. The methods used to achieve these goals include mathematical and statistical analysis, computer simulation and application to important datasets collected by cancer epidemiologists and other public health scientists.